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Department of Mathematics
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An introduction to Khovanov homology


Robert Todd


In this project we will learn the prerequisites to understanding and computing the Khovanov homology of a link. This includes: exact sequences of vector spaces over the rational numbers, computing homology with matrices, computing examples of homotopic maps, knots, knot diagrams, Reidemiester moves and invariance, the Jones polynomial, and it's categorification. This project will end with the computation of several difficult examples. Time permuting the extension of Khovanov homology to virtual knots will be discussed.